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Electronic structure of La 2-x Sr x CuO 4 calculated by the self-interaction correction method. Yoshida Laboratory Mino Yoshitaka. Contents. Introduction Material properties of La 2-x Sr x CuO 4 (LSCO) Purpose of my study Calculation method Local density approximation (LDA)

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slide1

Electronic structure of

La2-xSrxCuO4 calculated by the

self-interaction correction method

Yoshida Laboratory

Mino Yoshitaka

contents
Contents
  • Introduction
    • Material properties of La2-xSrxCuO4 (LSCO)
    • Purpose of my study
  • Calculation method
    • Local density approximation (LDA)
    • Self-Interaction Correction (SIC)
  • Results
    • Calculated electronic structure of LSCO
    • Stability of anti-ferromagnetic state

(The calculation code is MACHIKANEYAMA and the SIC program is developed by Toyoda.)

  • Discussion
  • Summary
  • Future work
introduction
Introduction

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

La2CuO4

AFM :anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

La

Oz

Oxy

Cu

introduction1
Introduction

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

La2CuO4

La2-xSrxCuO4

AFM :anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

TN:200~300 K

La

x=0.02

  • La2CuO4 is one of the transitional-metal oxides (TMO).
  • The electronic structure of the TMO is not well described by the band structure method based on the local density approximation (LDA)
  • The purpose of my study is to reproduce the magnetic phase diagram with the self-interaction correction (SIC) method in the first principle calculation.

Oz

Oxy

Cu

kohn sham theory
Kohn-Sham theory

We map a many body problem on one electron problem with effective potential.

Schrodinger equation

Kohn-Sham equation

veff(r) : effective potential

ψi(r) : wave function

ψi(r)

veff(r)

W. Kohn, L. J. Sham ; Phys. Rev. 140, A1133 (1965)

local density approximation lda
Local Density Approximation (LDA)
  • We do not know the μxcand we need approximate expressions of them to perform electronic structure calculations.
  • For a realistic approximation, we refer homogeneous electron gas.

Local Density Approximation (LDA)

When the electron density changes in the space, we assume that the change is moderate and the electron density is locally homogeneous.

External potential

Coulomb potential from electron density

effective potential

We call this “exchange correlation potential”.

systematic error of lda
Systematic error of LDA

LDA has some errors in predicting material properties.

  • Underestimation of lattice constant.
  • Overestimation of cohesion energy.
  • Overestimation of bulk modulus.
  • Underestimation of band gap energy.
  • Predicting occupied localize states (d states) at too high energy.
  • ...
self interaction correction sic
Self-interaction correction(SIC)

External potential

Coulomb interaction between electrons

exchange correlation potential

effective potential

LDA

Self Coulomb interaction and self exchange correlation interaction don’t cancel each other perfectly.

We need self-interaction correction (SIC) .

J. P. Perdew, Alex Zunger; Phys. Rev. B23, 5048 (1981)

Alessio Filippetti and Nicola A. Spaldin; Phys. Rev. B67, 125109 (2003)

dos of la 2 cuo 4 by lda and by sic lda
DOS of La2CuO4 by LDA and by SIC-LDA

LDA

LDA: non-magnetic and metallic.

SIC: anti-ferromagnetic and insulating:

local magnetic moment on Cu: 0.53 μB

band gap: about 0.8 eV

Exp: anti-ferromagnetic and insulating:

Cu local magnetic moment: 0.3 ~ 0.5 μB

band gap: about 0.9 eV

Cu 3d

O 2p

Cu 3d

anti-ferromagnetism with SIC-LDA

Cu 3d

O 2p

Cu 3d

Cu 3d

T. Takahashi et al ; Phys. Rev. B 37, 9788 (1988)

type of the insulator of transition metal oxide
Type of the insulatorof transition metal oxide

Ud

charge transfer insulator:

Ud > Δ

(La2CuO4)

Δ

LH d state

p state

UH dstate

E

Ud

Mott-Hubbard insulator:

Ud < Δ

LH d state

p state

UH d state

E

Δ

the magnetic p hase diagram
The magnetic phase diagram

The stability of anti-ferromagnetic state

The energy difference between paramagnetic and anti-ferromagnetic state.

La2-xSrxCuO4

:Cu

The random system is calculated by Coherent Potential Approximation (CPA)

AFM :anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

x=0.02

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

stability of anti ferromagnetic state
Stability of anti-ferromagnetic state

La2-xSrxCuO4

Experimental result of x

The anti-ferromagnetism becomes unstable by hole doping.

the doping dependence with sr
The doping dependence with Sr

anti-ferromagnetism (x=0)

anti-ferromagnetism (x=0.16)

Cu 3d

O 2p

Sr 5p

Cu 3d

O 2p

La2-xSrxCuO4

anti-ferromagnetism (x=0.06)

  • Holes are doped in O 2p state
  • → Fermi level comes close to the valence band.
  • At x=0.16, the Fermi level comes into the valence band.

Sr 5p

Cu 3d

O 2p

super exchange interaction
Super exchange interaction

EF

dstate

A

E

A site

dstate

anti-ferromagnetic

A

B

dstate

B site

E

B

dstate

p d exchange interaction
p-d exchange interaction

EF

A

B

dstate

pstate

E

pstate

dstate

ferromagnetic.

The p-hole with up spin runs around in the crystal.

EF

dstate

E

A

B

pstate

dstate

pstate

summary
Summary
  • The electronic structure is not reproduced by the LDA.
  • The anti-ferromagnetic state of La2CuO4 is well reproduced by the SIC method.
  • The trend of the stability of the anti-ferromagnetism has been reproduced by using the SIC method.

future work

  • I will estimate the Neel temperature with the Monte Carlo simulation.
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